What is termed as the smallest angle between the radius vector and the x-axis?

The smallest angle between the radius vector and the x-axis is referred to as the reference angle. This concept is crucial in trigonometry and is defined as the acute angle formed by the terminal side of an angle and the x-axis. The reference angle is always positive and is measured in the counterclockwise direction from the x-axis to the radius vector. It provides a way to simplify the analysis of the angles and their corresponding trigonometric functions across different quadrants.

Understanding the reference angle helps in solving various trigonometric problems, as it allows for the determination of sine, cosine, and tangent values for angles beyond the first quadrant by relating them back to their corresponding acute angles. This characteristic makes the reference angle an important tool in geometry and calculus when analyzing circular motion, periodic functions, and angle relationships.